1. Field of the Invention
The invention relates generally to a wrist mechanism for a robotic manipulator. In particular, the invention relates to a wrist mechanism having kinematically zero length and mutually orthogonal unlimited joints thus enabling to access any reachable point from any arbitrary direction.
2. Description of the Related Art
The dexterity of a robotic manipulator has been defined as the ability of a manipulator to access a point in a workspace from different directions. This ability is a function of the link dimensions and the joint limits of the robotic manipulator.
In order for a robotic manipulator to access every point in the workspace from all directions, three criteria must be met, including (i) three wrist joints having unlimited rotatability, (ii) three wrist joint axes intersecting at a mutually orthogonal point, and (iii) a point of intersection of the wrist axes being located at the tip of an end effector. It is the latter criteria that appears most difficult to practically achieve using current systems.
Thus, current robotic manipulators are not capable of accessing every point in the workspace from all directions due to wrist link parameters that may be impractical to obtain using current designs.
The implementation of robotic manipulators and Computer Numerically Controlled (CNC) machines generally requires the end effector of the manipulator to follow a specified trajectory. This trajectory requires the end effector to visit various points in Cartesian space as well as to access these points from arbitrary directions. Accessing a point from an arbitrary direction requires the manipulator to have six degrees of freedom, three for position and three for orientation. This being the case, most manipulators are constructed with six axes. The axes of the manipulator are either revolute joints or prismatic joints.
Also, in robotic manipulators and CNC systems, the manipulator consists of a regional structure and a wrist structure. The regional structure consists of a first set of three links for global positioning and the wrist structure consists of a last set of three links for orientation. In these systems the regional structure is relatively large compared to the wrist structure.
With the trajectory specified, the joint values need to be calculated for each point along the trajectory. This is called the inverse kinematics problem. A closed form solution to the inverse kinematics problem is difficult, if not impossible, to find for a generalized manipulator. This is due to the highly non-linear nature of the equations used to describe the kinematics of the manipulator. If a closed form solution cannot be found, the inverse kinematics must be solved numerically and the time required for computing the inverse kinematics may prevent real time trajectory planning. In light of these obstacles, most manipulators have a "simple" design which allows for finding a closed form solution for the inverse kinematics thereby allowing for real time trajectory planning.
One feature of a simple design is to have the last three axes intersect at a point which is located at the center of the wrist, but not at the end effector. However, even with a simple design, not all the points in the manipulator's reachable workspace can be accessed from any arbitrary direction. This is typically due to the length of the last link of the manipulator.
The inverse kinematics becomes decoupled and more efficiently solved if the wrist structure is designed so that the center of the wrist is located at the end effector. Moreover, all reachable points can be accessed from any arbitrary direction if all of the wrist joints are unlimited. Kinematically, a wrist with such a design has zero dimension.
Some attempts have been made to design a zero dimension wrist. For example, Fayet and Jutard have designed a manipulator which consists of three bar linkages within the regional structure. In this design, the linkages within the regional structure allow the mount of the end effector to maintain a fixed orientation with respect to the base of the manipulator. Thus, as the regional structure is moved for global positioning, the orientation of the mount remains fixed. The orientation of the end effector is then achieved by varying the joints of the wrist.
Another approach has been suggested by Nguyen, et. al. which replaces the wrist structure with a Steward platform. Although these designs have advantages for solving the inverse kinematics problem, the wrists have limited ranges of motion and thus cannot access every reachable point from any arbitrary direction.
One method for overcoming the shortcomings of Fayet and Jutard, and Nguyen, is to replace the intermediate joint of a Euler angle wrist with a linkage. To this end, Guinot and Biduad have replaced the intermediate joint with a Peaucellier inversor mechanism.
Another design based on this concept was developed by Mosher and used by Pilarski and Trevelyan. The Mosher design consists of replacing the intermediate joint of a Euler angle wrist with two four-bar linkages in series. This design achieves the zero dimension, but has a very limited range of motion which introduces a dwell time when the angle of the intermediate wrist joint passes through the zero position.
FIG. 1 shows the Mosher design. As seen in FIG. 1, the wrist mechanism consists of two parallelogram four-bar linkages in series. The outermost link 6 rotates about a tool tip. This results in three axes of the linkage intersecting at the tool tip. However, this mechanism has a limited range of motion for the intermediate joint .theta..sub.5, e.g., 0.ltoreq..theta..sub.5 .gtoreq.120.degree.. Also, this configuration creates a dwell time problem when the joints are rotated through the zero position. Particularly, the dwell time occurs when .theta..sub.4 and .theta..sub.6 axes are rotated 180.degree., while .theta..sub.5 is held at 0.degree.. This occurs before .theta..sub.5 can continue in the negative range. As further seen in FIG. 1, all of the bars are contained in four planes of motion, namely, the fixed side bar 1 in a first plane, side bars 2 and 4 positioned on a second plane and side bars 3 and 5 positioned on a third plane, and a coupler bar 6 is positioned in a fourth plane. The design of Mosher (and others, e.g., Guinot and Biduad) have unlimited ranges of motions for the first and last joints, but have limited ranges of motion for the intermediate joint. This reduces the amount of movement of the wrist mechanism.
An improvement to these designs would include a wrist mechanism having an unlimited range of motion for the intermediate joint. Such a design would allow accessing any reachable point from any arbitrary direction and eliminating the dwell time problem. The inverse kinematics would also be solved more efficiently, thus allowing for real time trajectory planning.